$11-2\mathrm{.}24.$ The segment of road passing over the crest of a hill is defined by the parabolic curve $y=0\mathrm{.}4x-0\mathrm{.}01x^2.$ A car weighing $3220lb$ travels along the road at a constant speed of $30fps.$ What is the normal pressure on the wheels of the car when it is at the crest of the hill where $y=4ft?$ At what speed will the road pressure be zero?

Hint: The radius of curvature is defined by

$=\frac{[1+(\frac{dy}{dx}{)}^2{]}^{\frac{3}{2}}}{\frac{d^{2}y}{d{x}^2}}$

$11-2\mathrm{.}25.$ As a car passes jver the crest of the hill described in the previous problem, the brakes are locked and the wheels skid. The tangential

retardation produced is $0\mathrm{.}4g.$ If the coefficient of friction between the tires and the road is $0\mathrm{.}70,$ how fast is the car moving?